Multivariate equivalent of ICC?

This isn't concerning OpenMx per se, but rather a general twin analysis question.

My variables are PC scores from a decomposition of shape data. Normally for one variable, you'd calculate an ICC for MZ and DZ groups to show if there is greater similarity for MZ's, prior to more formal modelling. My data needs to be analysed together instead of testing each variable/PC separately. Is there a multivariate equivalent of the ICC - ie something like partial least squares or canonical correlations?

On the whole we use SEM for both univariate and multivariate twin analysis, and do not use the ICC as a statistic. By constraining the variances of twin 1 and twin 2 to be equal, an equivalent statistic is estimated. If the raw data frame is used for input, missing data are handled appropriately as well. Multivariate analysis is much more likely to have missing data, be it from an unmatched twin or one or two of the observed variables, hence direct analysis of the raw data is usually the best way to go.